anonymous
  • anonymous
Find the greatest 4 digits number which when divided by 18,24,30 and 36 leaves a remainder 17 (in each case).
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
amoodarya
  • amoodarya
a=18q+17 a=24k+17 a=30p+17 so 30|a-17 24|a-17 18|a-17 so [24,18,30]|a-17
anonymous
  • anonymous
I need a way by which I can calculate answer to such question in 1-2 mins time. This type of questions appears in admission exam for MS(CS).
anonymous
  • anonymous
no offense but @amoodarya I got no clue what you did back there. A little explanation please ?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

UsukiDoll
  • UsukiDoll
that notation for the second one is 30 divides a -17 similarly 24 divides a-17 and 18 divides 1-17
ganeshie8
  • ganeshie8
Let \(a\) = required number Notice that \(a-17\) is divisible by each of the given integers, therefore \(a-17\) must also be divisible by their lcm, \(360\) : \[a-17 = 360k\]
amoodarya
  • amoodarya
[30,24,18]=[5.3.2, 2.2.2.3, 3.3.2]=2.2.2.3.3.5=\[2^3*3^2*5=360\\a-17=360k\\a=360k+17\\a_\min=360*3+17=1080+17\]
anonymous
  • anonymous
@ganeshie8 and others thank you!
UsukiDoll
  • UsukiDoll
when did k =3 for the last line? just wondering. unless we have k = 3 because it's the lcm of 18,24,30, and 36.
anonymous
  • anonymous
Lol I think @amoodarya assumed k = 3 :P
UsukiDoll
  • UsukiDoll
:S there is always a reason to let k = 3. isn't it?
anonymous
  • anonymous
I can't think of any reasons to do so :| cause 3 isn't given in the question
UsukiDoll
  • UsukiDoll
the only thing I can think of is that 3 is the lcm of 18.24.30.36.. not to mention that's part of the 3 x table 3 x 6 =18 3 x 8 = 24 3 x 10 = 30 3 x 12 = 36 3 x 3 x 2 = 18 3 x 2 x 2 x 2 = 24 3 x 2 x 5 = 30 3 x 3 x 2 x 2 Each of them has at least 1 3
anonymous
  • anonymous
yup thats true
anonymous
  • anonymous
@amoodarya it'll be less confusing if you just type down a few words explaining the problem like ganeshie8 did. Thanks
amoodarya
  • amoodarya
\[a=360k+17 \ge 1000\\360k \ge 1000-17\\k \ge \frac{1000-17}{360}\\k \space is \space integer \\k \ge 3\]
UsukiDoll
  • UsukiDoll
where did you get the 1000 from?
anonymous
  • anonymous
largest 4 digit number is 9999 Man Imma cry now seriously
anonymous
  • anonymous
@amoodarya you're not helping sir rather you are making it more confusing and complex :|
UsukiDoll
  • UsukiDoll
yeah this is how my adviser would do... just be like ok this this this the end.
anonymous
  • anonymous
LOL I hate such kind of teachers >:| Teacher's job is to explain the whole process....
UsukiDoll
  • UsukiDoll
yeah I got a B- for absolutely knowing 5.5 out of 8 chapters in Passage to Advanced Mathematics book
amoodarya
  • amoodarya
oh . sorry i had a little mistake i wrote it for smallest 4 digits so you do it for the greatest , like that
anonymous
  • anonymous
@ganeshie8 can you make things simple its seriously frying my brain :|
UsukiDoll
  • UsukiDoll
wow I wish my retired professor was on here. He was awesome.
ganeshie8
  • ganeshie8
spoonfeeding is not good always, it would be more fun if you try and solve the problem on your own based on the given hints
amoodarya
  • amoodarya
\[a \leq 9999\\360k+17 \leq 9999\\k \leq \frac{9999-17}{360}\]
UsukiDoll
  • UsukiDoll
well what if the person made so many attempts and then got fed up?
ganeshie8
  • ganeshie8
where are the "many" attempts ?
anonymous
  • anonymous
^ yes that's what I am doing for last 1 hour :|
UsukiDoll
  • UsukiDoll
k is less than or equal to 27.7222222222 something seems legit
UsukiDoll
  • UsukiDoll
"many" attempts? lol like using every theorem out there
ganeshie8
  • ganeshie8
teaching is not easy... there is no way for a teacher to know what the student has already tried right
UsukiDoll
  • UsukiDoll
showing off like what my professor did to me a while back doesn't help me understand either -_-
anonymous
  • anonymous
^
ganeshie8
  • ganeshie8
try this : teach me how to multiply 3*5
UsukiDoll
  • UsukiDoll
ummm let's see. it's like writing 3 5 times and adding them up
anonymous
  • anonymous
3*5 = 15 simple enough :O
ganeshie8
  • ganeshie8
how do you know i know addition ?
UsukiDoll
  • UsukiDoll
omg! take 3 rocks that's 1 batch then 3 rocks 3 rocks 3 rocks 3 rocks... add them all up
anonymous
  • anonymous
alright I'll solve it myself .... no more arguments
ganeshie8
  • ganeshie8
where do i find rocks ? your explanation is confusing me
UsukiDoll
  • UsukiDoll
you find rocks outside!
amoodarya
  • amoodarya
|dw:1435484624755:dw|
UsukiDoll
  • UsukiDoll
or buy them or find them at a park or at your house
ganeshie8
  • ganeshie8
now that i don't want to buy rocks, why do i need rocks ? how are they related to multiplications
anonymous
  • anonymous
OMG thats childish @ganeshie8 :| @amoodarya 's work was confusing me because he took the question wrongly.
UsukiDoll
  • UsukiDoll
don't want to buy rocks ! BORROW MARBLES FROM YOUR FRIEND!
anonymous
  • anonymous
I'm outta here seriously....
ganeshie8
  • ganeshie8
so i need to have a friend to understand multiplcations ?
UsukiDoll
  • UsukiDoll
-_-! you have none.. draw circles on paper.
ganeshie8
  • ganeshie8
Okay enough, we're not getting anywhere. I hate math and you're the reason for that.
UsukiDoll
  • UsukiDoll
wow... then you as a student fail then
ganeshie8
  • ganeshie8
isn't that obvious
UsukiDoll
  • UsukiDoll
*rolls eyes* why waste my time with gibberish? If you still don't understand it after so many tries, it becomes useless to the point that the only way to solve this issue to just fail the student and send it to summer school.
ganeshie8
  • ganeshie8
same thing can repeat in summer school
UsukiDoll
  • UsukiDoll
then why should the student still be in school then? Have it kicked out of the system and force it to get a job.
ganeshie8
  • ganeshie8
more or less, thats the story of most school dropout these days right one bad/annoying teacher is all it takes
UsukiDoll
  • UsukiDoll
not the teacher's fault really. It's the student. If they are not committed...don't bother... just do something productive with life and that's it.
ganeshie8
  • ganeshie8
you(teacher) failed to teach me(3rd grade kid) how to multiply
UsukiDoll
  • UsukiDoll
-_-! No you failed yourself.
ganeshie8
  • ganeshie8
more than that, you killed my confidence and love of math
UsukiDoll
  • UsukiDoll
and you have gotten really annoying after a while.
ganeshie8
  • ganeshie8
hmm
UsukiDoll
  • UsukiDoll
annas and amoodarya got it right. It was just you !
ganeshie8
  • ganeshie8
aren't we role modeling anymore, you as a good teacher and me as a poor student ?
UsukiDoll
  • UsukiDoll
KNOCK IT OFF ALREADY!
ganeshie8
  • ganeshie8
Okay fine
UsukiDoll
  • UsukiDoll
and it's role playing...
anonymous
  • anonymous
It's a fault on both ends cause our teachers now a days are not as determined as they used to be in 90's and our students shows no seriousness in studies. Well it is kind of a fault of teachers, a good teacher always try to develop interest of his/her students in the subject. Our education system is faulty and teacher's only see teaching as a profession and nothing else.... Sad story!
UsukiDoll
  • UsukiDoll
geez... this is not helping annas at ALL! What started out as trying to clarify things turned into stupid stuff that is NONSENSE AND OFF TOPIC!
ganeshie8
  • ganeshie8
I agree annas, its always the fault of teacher.
UsukiDoll
  • UsukiDoll
what about favoritism?
anonymous
  • anonymous
@ganeshie8 I am not a 2 year old to be spoon feed I know maths very well... Only problem is I dont remember basic stuff cause of lack of practice. And I am doing this basic stuff just for a stupid test for admission in MS. I've an interview related to my field i.e. software engineering but to qualify for that I need to clear this stupid test... The only reason to ask this question...
UsukiDoll
  • UsukiDoll
that's it... @Michele_Laino Help :*(
anonymous
  • anonymous
Favoritism is another issue in our education system... Teachers give marks for free to those students that they think are most favorite... It's a flaw of teacher AGAIN. I hate this current education system.
ganeshie8
  • ganeshie8
i think we're done with the original main q ?
anonymous
  • anonymous
Oh I solved the question on my own thank you @UsukiDoll answer I got was 9989. @ganeshie8 I didnt start all this discussion all I was asking is for some clarification.
ganeshie8
  • ganeshie8
9989 is wrong are you still looking for clarification ? what part do you not understand in ammodarya's solution ?
UsukiDoll
  • UsukiDoll
@annas I know a good example that happened at my university remembered that annoying professor I had for that Intro to Advanced Mathematics class? he gave me a B- which was surprising because like I said I only mastered 5.5 out of 8 chapters. Fast forward to a year later... some girl had the same professor and ended up almost failing like a D- Keep in mind that annoying professor happens to be my undergrad. adviser.
ganeshie8
  • ganeshie8
\(a = 360k+17\) Is it hard to solve \(k\) that gives the maximum \(4\) digit number ?
anonymous
  • anonymous
I was taking k = 27.7 now I took k = 27 and I got 9737
ganeshie8
  • ganeshie8
thats looks correct
anonymous
  • anonymous
Alright, thanks
ganeshie8
  • ganeshie8
yw, the dicussion was not so fruitful but i enjoyed it thanks!

Looking for something else?

Not the answer you are looking for? Search for more explanations.